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Unit 3: Modeling a System

Karl Kreutz (University of Maine), Deborah Gross (Carleton College), and Lisa Gilbert (Williams College)

These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below. Visit InTeGrate and the NGSS to learn more.

Overview

Students are introduced systems modeling, which allows system components to be quantified and manipulated to demonstrate system response. Students use a simple systems model of a bathtub to explore the effect of flow rates on system equilibrium.

Science and Engineering Practices

Developing and Using Models: Evaluate limitations of a model for a proposed object or tool. MS-P2.1:

Developing and Using Models: Develop or modify a model— based on evidence – to match what happens if a variable or component of a system is changed. MS-P2.2:

Developing and Using Models: Develop and/or revise a model to show the relationships among variables, including those that are not observable but predict observable phenomena. MS-P2.4:

Developing and Using Models: Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system HS-P2.3:

Developing and Using Models: Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems. HS-P2.6:

Cross Cutting Concepts

Systems and System Models: Models can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy, matter, and information flows within systems. MS-C4.2:

Systems and System Models: When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. HS-C4.2:

Systems and System Models: Systems can be designed to do specific tasks. HS-C4.1:

Systems and System Models: Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. HS-C4.3:

Stability and Change: Systems can be designed for greater or lesser stability. HS-C7.4:

Stability and Change: Much of science deals with constructing explanations of how things change and how they remain stable. HS-C7.1:

Stability and Change: Feedback (negative or positive) can stabilize or destabilize a system. HS-C7.3:

Stability and Change: Change and rates of change can be quantified and modeled over very short or very long periods of time. Some system changes are irreversible. HS-C7.2:

This material was developed and reviewed through the InTeGrate curricular materials development process. This rigorous, structured process includes:

  • team-based development to ensure materials are appropriate across multiple educational settings.
  • multiple iterative reviews and feedback cycles through the course of material development with input to the authoring team from both project editors and an external assessment team.
  • real in-class testing of materials in at least 3 institutions with external review of student assessment data.
  • multiple reviews to ensure the materials meet the InTeGrate materials rubric which codifies best practices in curricular development, student assessment and pedagogic techniques.
  • review by external experts for accuracy of the science content.

This activity was selected for the On the Cutting Edge Exemplary Teaching Collection

Resources in this top level collection a) must have scored Exemplary or Very Good in all five review categories, and must also rate as “Exemplary” in at least three of the five categories. The five categories included in the peer review process are

  • Scientific Accuracy
  • Alignment of Learning Goals, Activities, and Assessments
  • Pedagogic Effectiveness
  • Robustness (usability and dependability of all components)
  • Completeness of the ActivitySheet web page

For more information about the peer review process itself, please see http://serc.carleton.edu/NAGTWorkshops/review.html.



This page first made public: Oct 24, 2016

Summary

This unit introduces systems modeling, which allows students to quantify and manipulate system components to create system responses. Students use a simple systems model of a bathtub to explore the effect of flow rates on system equilibrium. To complete the unit, students will need a method for creating and sharing diagrams (whiteboards, posters, etc.), and will ideally have access to free systems modeling software.

Learning Goals


  • Students will be able to apply systems vocabulary to the structure of a systems model.
  • Students will be able to contrast conditions that produce equilibrium and non-equilibrium behavior in a systems model.
  • Students will be able to estimate residence time for a system in equilibrium.

Context for Use

This unit should ideally occur mid-course, after students have been introduced to systems thinking concepts in Units 1 and 2. Unit 3 uses a dynamical system model developed with the STELLA software package. Depending on class setting, instructors have three different approaches for accessing the Bathtub Model (Stella Model (v10 .stmx) 9kB Jan3 17) with students: 1) instructors can use the

Systems modeling experiment notes PowerPoint


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

(also available as a
PDF


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

), which contains all the necessary images of model structure, interface, and output. This approach requires no STELLA software; 2) instructors can run model experiments on their device, and display to the class for discussion; or 3) students can run model experiments on their devices, either individually or in groups, and the instructor can decide how to facilitate discussion.

This unit may fit into a single 50-minute class period, assuming efficient use of time (i.e., the instructor runs the models [or uses the model images] and displays output for discussion with students, or students come to class with software resources installed and running properly). Student use of models may lead to more in-depth discussion, and will likely also mean the unit requires multiple class periods. Finally, the instructor and students may, if they have the STELLA software package, decide to explore, modify, and/or expand the models in any number of ways; this also would require multiple class periods.

Description and Teaching Materials

If instructors choose to use STELLA software (approach 2 or 3 from above), different options are available depending on classroom setting, platform, and financial considerations.

  • Download and install the free isee Player software available in Windows and Macintosh versions. Models can be run and output interpreted with Player. Units 3 and 4 can be completed with Player software alone.
  • Purchase, download, and install STELLA software available in Windows and Macintosh versions. Models can be run and output interpreted with STELLA; models can also be modified, output saved, and shared with STELLA.
  • Purchase, download, and install the STELLA Modeler for iPad software (also available from the Apple App Store). Models can be run and output interpreted with Modeler for iPad; models can also be modified, output saved, and shared with Modeler for iPad.

Students will need to develop and share diagrams in class; this can be done via whiteboard, large Post-it notes, paper, or electronically. They will also need to complete the Systems modeling worksheet Word doc (Microsoft Word 80kB Sep12 16) (also available as a PDF (Acrobat (PDF) 74kB Sep12 16)), which can be done electronically or as a handout.

The Systems modeling quick start PowerPoint (PowerPoint 2.3MB Jan3 17) (also available as a PDF (Acrobat (PDF) 1.9MB Jan3 17)) has instructions on how to get started using Bathtub Model (Stella Model (v10 .stmx) 9kB Jan3 17). If students will be using Player or STELLA software, they should download the software and review the quick start prior to class.

*Note that the STELLA model and model images used in this unit were created with STELLA Architect v.1 software.

Part 1. Pre-experiment discussion of systems models (20 min)

Begin class with an instructor-led review of the systems concepts covered in Unit 1 and 2, namely inflow, reservoir, and outflow. Next, introduce systems models using the Systems modeling presentation PowerPoint (PowerPoint 4.2MB Jan3 17) (also available as a PDF (Acrobat (PDF) 4.2MB Jan3 17)). Afterward, if time allows, ask each student/group to identify a single inflow/reservoir/outflow component within the system diagram they developed in Unit 2 (either the group diagrams developed in class, or the homework diagrams developed individually). On a sketch, students/groups should draw the component structure, identify units for the flows and reservoir, and make rough but realistic estimates of flux and reservoir values. Have students/groups share their sketches and ideas with the class. Focus particular attention on distinguishing reservoir examples that may be changing with time from those that are not.

Part 2. Experiment 1 — Equilibrium vs. non-equilibrium (10 min)

  • Students should use the Systems modeling worksheet Word doc (Microsoft Word 80kB Sep12 16) (also available as a PDF (Acrobat (PDF) 74kB Sep12 16)) to walk through the experiment. Ideally this would be done in small groups, so that students can work together to answer questions about model output. The instructor can encourage whole class discussion of findings.
    • Experiment 1a: Run Bathtub Model (Stella Model (v10 .stmx) 9kB Jan3 17) with the following parameters: Faucet = 1 liter/second; Drain = 1 liter/second; Water in bathtub = 10 liters; Discuss results, namely that when inflow and outflow are balanced, the reservoir size does not change with time. Hence, the system is in equilibrium.
    • Experiment 1b: Run Bathtub Model (Stella Model (v10 .stmx) 9kB Jan3 17) with the following parameters: Faucet = 2 liters/second; Drain = 1 liter/second; Water in bathtub = 10 liters; Discuss results, where inflow and outflow are not balanced. The reservoir size changes with time (increasing linearly in this case), and the system is therefore in non-equilibrium.
  • The instructor should encourage whole class discussion of findings. Model images and discussion notes for instructors are in the
    Systems modeling experiment notes PowerPoint


    This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

    (also available as a
    PDF


    This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

    ).

Part 3. Experiment 2 — Residence time (10 min)

  • Students should use the Systems modeling worksheet Word doc (Microsoft Word 80kB Sep12 16) (also available as a PDF (Acrobat (PDF) 74kB Sep12 16)) to walk through the experiment. Ideally this would be done in small groups, so that students can work together to answer questions about model output.
    • Experiment 2a: Run Bathtub Model (Stella Model (v10 .stmx) 9kB Jan3 17) with the following parameters: Faucet = 1 liter/second; Drain = 1 liter/second; Water in bathtub = 10 liters; Explain residence time concept, and discuss how to calculate residence time for this model run (residence time here = 10 seconds).
    • Experiment 2b: Run Bathtub Model (Stella Model (v10 .stmx) 9kB Jan3 17) with the following parameters: Faucet = 2 liters/second; Drain = 2 liter/second; Water in bathtub = 10 liters; Discuss results, namely that the system is still in equilibrium even though fluxes are doubled (and balanced). Calculate residence time (5 seconds in this case), compare to previous run, and discuss implications of residence time changes for any system including real-world examples.
  • The instructor should encourage whole class discussion of findings. Model images and discussion notes for instructors are in the
    Systems modeling experiment notes PowerPoint


    This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

    (also available as a
    PDF


    This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

    ).

Part 4. Homework

  • As a summative assessment, students are asked to consider a simple inflow/reservoir/outflow system that they likely encounter every day (a parking lot) in the Systems modeling homework Word doc (Microsoft Word 43kB Sep12 16) (also available as a PDF (Acrobat (PDF) 58kB Sep12 16)). Questions emphasize equilibrium, non-equilibrium, and residence time concepts.

Teaching Notes and Tips

While Unit 3 can be done using the model images in the experiment notes alone, we highly recommend using the models interactively in class — the models can be run repeatedly to reinforce concepts, and the instructor (and students) can easily and quickly navigate between different model levels (e.g., interface and model levels).

If students will use models in class, they should have the software installed and models downloaded prior to class. They should also use the Systems modeling quick start PowerPoint (PowerPoint 2.3MB Jan3 17) (also available as a PDF (Acrobat (PDF) 1.9MB Jan3 17)) to become familiar with basic model controls prior to class.

Assessment

  • To assess student comprehension during the unit, instructors can collect the Systems modeling worksheet Word doc (Microsoft Word 80kB Sep12 16) (also available as a PDF (Acrobat (PDF) 74kB Sep12 16)) after class.
    • An answer key is provided here as a
      Word doc


      This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

      or
      PDF


      This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

      .
  • The Systems modeling homework Word doc (Microsoft Word 43kB Sep12 16) (also available as a PDF (Acrobat (PDF) 58kB Sep12 16)) assignment provides an opportunity to assess whether students have developed a basic understanding of systems models, how to apply systems vocabulary, and equilibrium and residence time concepts.
    • An answer key for the homework is provided here as a
      Word doc


      This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

      or
      PDF


      This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

      .
    • A suggested rubric for evaluating student responses is here as a
      Word doc


      This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

      or
      PDF


      This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

      .

References and Resources

STELLA modeling resources

  • Shiflet, A.B., and Shiflet, G.W., 2006, Introduction to Computational Science: Modeling and Simulation for the Sciences, Princeton University Press. Contains excellent basic tutorials on using STELLA software
  • How to Read a STELLA Model Diagram, from CC Modeling Systems, has a basic instruction to STELLA model diagrams
  • iSee Systems' Community page has a number of useful resources related to dynamic system modeling
  • iSee Systems' Book Store has a number of books available on dynamic system modeling

System equilibrium and growth/decay

Residence time

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These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. The materials engage students in understanding the earth system as it intertwines with key societal issues. The collection is freely available and ready to be adapted by undergraduate educators across a range of courses including: general education or majors courses in Earth-focused disciplines such as geoscience or environmental science, social science, engineering, and other sciences, as well as courses for interdisciplinary programs.
Explore the Collection »